Average Error: 0.0 → 0.0
Time: 16.6s
Precision: 64
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[\mathsf{fma}\left(i, c, \left(\mathsf{fma}\left(a, b, \left(\mathsf{fma}\left(x, y, \left(t \cdot z\right)\right)\right)\right)\right)\right)\]
\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i
↓
\mathsf{fma}\left(i, c, \left(\mathsf{fma}\left(a, b, \left(\mathsf{fma}\left(x, y, \left(t \cdot z\right)\right)\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2035372 = x;
        double r2035373 = y;
        double r2035374 = r2035372 * r2035373;
        double r2035375 = z;
        double r2035376 = t;
        double r2035377 = r2035375 * r2035376;
        double r2035378 = r2035374 + r2035377;
        double r2035379 = a;
        double r2035380 = b;
        double r2035381 = r2035379 * r2035380;
        double r2035382 = r2035378 + r2035381;
        double r2035383 = c;
        double r2035384 = i;
        double r2035385 = r2035383 * r2035384;
        double r2035386 = r2035382 + r2035385;
        return r2035386;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2035387 = i;
        double r2035388 = c;
        double r2035389 = a;
        double r2035390 = b;
        double r2035391 = x;
        double r2035392 = y;
        double r2035393 = t;
        double r2035394 = z;
        double r2035395 = r2035393 * r2035394;
        double r2035396 = fma(r2035391, r2035392, r2035395);
        double r2035397 = fma(r2035389, r2035390, r2035396);
        double r2035398 = fma(r2035387, r2035388, r2035397);
        return r2035398;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(i, c, \left(\mathsf{fma}\left(a, b, \left(\mathsf{fma}\left(x, y, \left(z \cdot t\right)\right)\right)\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(i, c, \left(\mathsf{fma}\left(a, b, \left(\mathsf{fma}\left(x, y, \left(t \cdot z\right)\right)\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))